Numerical simulation of drift-resistive ballooning turbulence in the presence of the GA mode in the plasma edge tokamak

Drift-resistive ballooning turbulence is simulated numerically based on a quasi-three-dimensional computer code for solving nonlinear two-fluid MHD equations in the scrape-off layer plasma in a tokamak. It is shown that, when the toroidal geometry of the magnetic field is taken into account, additional (geodesic) flux terms associated with the first poloidal harmonic (∼sinθ) arise in the averaged equations for the momentum, density, and energy. Calculations show that the most important of these terms is the geodesic momentum flux (the Stringer-Windsor effect), which lowers the poloidal rotation velocity. It is also shown that accounting for the toroidal field geometry introduces experimentally observed, special low-frequency MHD harmonics—GA modes—in the Fourier spectra. GA modes are generated by the Reynolds turbulent force and also by the gradient of the poloidally nonuniform turbulent heat flux. Turbulent particle and heat fluxes are obtained as functions of the poloidal coordinate and are found to show that, in a tokamak, there is a “ballooning effect” associated with their maximum in the weak magnetic field region. The dependence of the density, temperature, and pressure on the poloidal coordinate is presented, as well as the dependence of turbulent fluxes on the toroidal magnetic field.     

Polarization splitting of the Alfvén wave spectrum in a dipole magnetosphere with a rotating plasma

Alfvén waves in a dipole magnetosphere with a rotating plasma are studied theoretically. The plasma-motion-related properties of azimuthally small-scale standing Alfvén waves having nearly poloidal or nearly toroidal polarization are analyzed. Equations are obtained that describe the longitudinal (along the magnetic field) structure and spectra of the waves having such polarizations. The equations obtained are then solved both analytically (in the Wentzel-Kramers-Brillouin approximation) and numerically. Attention is focused on the polarization splitting of the spectrum—the difference between the eigenfrequencies of the toroidally and poloidally polarized Alfvén waves. The distribution of this difference in a direction across the magnetic shells is analyzed. It is shown that, unlike in the models in which the plasma is assumed to be at rest, taking into account rotation of the magnetosphere plasma results in an additional splitting of the spectrum of the poloidal Alfvén waves due to the difference in their azimuthal mode numbers.     

Measurements of the load resistance of a poloidal antenna and the phase velocity of fast magnetosonic waves during ICR plasma heating in the L-2M stellarator

The propagation and damping of waves excited by a poloidal antenna in a hydrogen plasma at the ion cyclotron resonance (ICR) frequency were investigated. The longitudinal wavenumber and damping length of waves excited in the ohmically heated plasma of the L-2M stellarator, the dependence of the damping length of fast magnetosonic waves on the magnetic field strength, and the dependence of the antenna load resistance on the plasma density were measured. It is the first time that such complex measurements were performed in experiments on ICR heating of a hydrogen plasma at the fundamental harmonic of the ion gyrofrequency in toroidal magnetic confinement systems.     

Characteristics of major plasma discharge disruption in the Globus-M spherical tokamak

The characteristics of the major disruption of plasma discharges in the Globus-M spherical tokamak are analyzed. The process of current quench is accompanied by the loss of the vertical stability of the plasma column. The plasma boundary during the disruption is reconstructed using the algorithm of movable filaments. The plasma current decay is preceded by thermal quench, during which the profiles of the temperature and electron density were measured. The data on the time of disruption, the plasma current quench rate, and the toroidal current induced in the tokamak vessel are compared for hydrogen and deuterium plasmas. It is shown that the disruption characteristics depend weakly on the ion mass and the current induced in the vessel increases with the disruption time. The decay rate of the plasma toroidal magnetic flux during the disruption is determined using diamagnetic measurements. Such a decay is a source of the poloidal current induced in the vessel; it may also cause poloidal halo currents.     

Radial electric field and rotation of the ensemble of plasma particles in tokamak

The velocity of macroscopic rotation of an ensemble of charged particles in a tokamak in the presence of an electric field has been calculated in a collisionless approximation. It is shown that the velocity of toroidal rotation does not reduce to a local velocity of electric drift and has opposite directions on the inner and outer sides of the torus. This result is supplemented by an analysis of the trajectories of motion of individual particles in the ensemble, which shows that the passing and trapped particles of the ensemble acquire in the electric field, on the average, different toroidal velocities. For the trapped particles, this velocity is equal to that of electric drift in the poloidal magnetic field, while the velocity of passing particles is significantly different. It is shown that, although the electric-field-induced shift of the boundaries between trapped and passing particles in the phase space depends on the particle mass and charge and is, in the general case, asymmetric, this does not lead to current generation.     

Effect of the radial electric field on the results of measurements of the poloidal rotation of a tokamak plasma by charge exchange recombination spectroscopy

Abtract The effect of the radial electric field E _r on the results of measurements of the poloidal rotation of a tokamak plasma by charge exchange recombination spectroscopy is considered. It is shown that the emission line shift arising from the finite lifetime of the excited state of the ions is proportional to E _r. For helium ions, the maximum shift corresponds to the poloidal rotation velocity, which is about one-third of the drift velocity in the crossed radial electric (E _r) and toroidal magnetic (B _t) fields. __________ Translated from Fizika Plazmy, Vol. 27, No. 11, 2001, pp. 1050–1052. Original Russian ? 2001 by Romannikov, Chernobai.     

Radial electric field during dynamic processes in a tokamak and L-H transitions

Expressions for the radial electric field in tokamaks are derived with allowance for an additional contribution of the longitudinal electron viscosity (or the associated Ware drift). It is shown that, in transient processes during which the toroidal electric field at the plasma edge increases, the additional electric field can become rather strong. An increase in the shear of the poloidal plasma rotation can trigger the L-H transition. That the experimentally observed transitions to an improved confinement mode can be ascribed to this effect is illustrated by simulating discharges in the current ramp-up experiments in the Tuman-3M tokamak.     

Diagnostics of MHD instability in the Globus-M spherical tokamak

The paper describes a diagnostic system for studying MHD plasma perturbations in the Globus-M spherical tokamak (a major radius of 0.36 m, a minor radius of 0.24 m, and an aspect ratio of 1.5). The system includes a poloidal and a toroidal array consisting of 28 and 16 Mirnov probes, respectively, as well as a 32-channel proportional soft X-ray detector. Methods are described for calculating the poloidal and toroidal numbers of the dominant helical perturbations by using data from probe measurements. Results are presented of processing the experimental data from some tokamak discharges with a plasma current of 150–250 kA, an average electron density of up to 10²⁰ m^?3, and a toroidal magnetic field of 0.4 T. Specific features of MHD perturbations and their influence on the parameters of the plasma column in different stages of a discharge are briefly discussed.     

On the possibility of reflection of Alfvén waves in a curvilinear magnetic field

The propagation of Alfvén waves in a plasma immersed in a curvilinear magnetic field is investigated by using a 2D model. The waves are described by a 1D equation that formally coincides with the equation for the case of a quasi-uniform straight magnetic field with a modified Alfvén velocity that takes into account the longitudinal dependence of the Lame coefficients. It is shown that toroidal and poloidal Alfvén modes depend differently on the magnetic-field geometry. In the case of a 2D plane-parallel configuration of the magnetic field, poloidal modes are efficiently reflected from regions where the magnetic field lines sharply converge or diverge. This effect can result in the formation of open-field-line Alfvén quasi-resonators.     

Study of plasma fluctuations in the Tuman-3m tokamak using microwave reflectometry with an obliquely incident probing beam

Plasma fluctuations in the Tuman-3M tokamak are studied experimentally by analyzing backscattered radiation for different angles of incidence of the probing beam from the normal to the cut-off surface. The poloidal rotation velocity of the plasma fluctuations is determined from the Doppler shift of the reflected radiation spectrum measured on the edge of the tokamak during the transition to the H-mode. It is shown that, before the transition to the H-mode, the rotation velocity can be estimated quantitatively from the spectral shift or from the rate at which the phase of the reflected signal grows. The experimental data obtained during the transition to the H-mode provide evidence for the onset of a sheared poloidal flow. The shear makes it difficult to correctly estimate the poloidal rotation velocity in the improved confinement regime. The main mechanisms responsible for the broadening of the backscattered radiation spectra are considered. The turbulent diffusion coefficients determined under the assumption that the spectral broadening is diffusive in character are found to be close to those determined from the charged-particle balance.     

Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field

The influence of a transverse magnetic field on the characteristics of the positive column of a planar low-pressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuous-medium model, while the ion motion in the ambipolar electric field is described by means of a kinetic equation. Using mathematical transformations, the problem is reduced to a secondorder ordinary differential equation, from which the spatial distribution of the potential is found in an analytic form. The spatial distributions of the plasma density, mean plasma velocity, and electric potential are calculated, the ion velocity distribution function at the plasma boundary is found, and the electron energy as a function of the magnetic field is determined. It is shown that, as the magnetic field rises, the electron energy increases, the distributions of the plasma density and mean plasma velocity become asymmetric, the maximum of the plasma density is displaced in the direction of the Ampère force, and the ion flux in this direction becomes substantially larger than the counter-directed ion flux.     

Stability and variations of plasma parameters in the L-2M stellarator during excitation of the induction current in the regime of ECR plasma heating

Results are presented from experimental studies of variations in the plasma parameters during the excitation of a multiaxis magnetic configuration by the induction current (up to 17 kA) in the basic magnetic configuration of the L-2M stellarator in the regime of ECR heating at a microwave power of ～200 kW (～1 MW m^?3) and an average plasma density of (1–2) × 10¹⁹ m^?3. The current direction was chosen to reduce the net rotational transform (the so-called “negative“ current). The current was high enough for the rotational transform to change its sign inside the plasma column. Computer simulations of the L-2M magnetic structure showed that the surface with a zero rotational transform is topologically unstable and gives rise to magnetic islands, i.e., to a multiaxis magnetic configuration. Magnetic measurements showed that, at negative currents above 10 kA, intense bursts of MHD oscillations with a clearly defined toroidal mode number n = 0 were observed in the frequency range of several kilohertz. Unfortunately, the experimental data are insufficient to draw the final conclusion on the transverse structure of these oscillations. The radial temperature profiles along the stellarator major radius in the equatorial plane were studied. It is found that the electron temperature decreases by a factor of 1.3 in the plasma core (r/a ≤ 0.6) and that the temperature jump is retained near the boundary. A change in turbulent fluctuations of the plasma density during the excitation of a negative current was studied using wave scattering diagnostics. It is found that the probability density function of the increments of fluctuations in the plasma core differs from a Gaussian distribution. The measured distribution is heavy-tailed and broadens in the presence of the current. It is found that the spectrum of turbulent fluctuations and their Doppler shift near the plasma boundary are nonuniform in the radial direction. This may be attributed to the shear of the poloidal velocity. The experimental results indicate that the formation of regions with a zero rotational transform in the plasma core somewhat intensifies plasma transport.     

The use of Doppler reflectometry in the L-2M stellarator

Results are presented from measurements of the plasma rotation velocity and plasma density fluctuations in the L-2M stellarator by the method of Doppler reflectometry. Specific problems that arise when applying this diagnostics to the stellarator are revealed. The poloidal plasma velocity at the periphery of the plasma column is determined. The results of measurements are well reproducible.     

Collisionless current generation in the center of the tokamak plasma by an isotropic source of α-particles

The density of the noninductive current generated due to collisionless motion of α-particles in the tokamak magnetic field is calculated. The analysis is based on fully three-dimensional calculations of charged particle trajectories without simplifying assumptions typical for drift and neoclassical approaches. The current is calculated over the entire cross section of the plasma column, including the magnetic axis. It is shown that the current density is not a function of a magnetic surface and is strongly polarized over the poloidal angle. The current density distribution in the tokamak poloidal cross section is obtained, and the current density as a function of the safety factor, the tokamak aspect ratio, and the ratio of the particle Larmor radius on the axis to the tokamak minor radius is determined. It is shown that, when the source of α-particles is spatially nonuniform, the current density in the center of the tokamak is nonzero due to asymmetry of the phase-space boundary between trapped and passing particles. The current density scaling in the tokamak center differs from the known approximations for the bootstrap current and is sensitive to the spatial distribution of α-particles.     

Neoclassical offset toroidal velocity and auxiliary ion heating in tokamaks

In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g., RF or any isotropic auxiliary heating) cannot give rise to net forces or torques. Experimental evidence on contemporary tokamaks shows that the near central absorption of RF heating power (ICH and ECH) and current drive in presence of MHD activity drives a bulk plasma rotation in the co-I _p direction, opposite to the initial one. Also the appearance of classical or neoclassical tearing modes provides a nonlinear magnetic braking that tends to clamp the rotation profile at the q-rational surfaces. The physical origin of the torque associated with P _RF absorption could be due the effects of asymmetry in the equilibrium configuration or in power deposition, but here we point out also an effect of the response of the so-called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity due to internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by kinetic and fluid calculations, that the absorption of auxiliary power by ions modifies this offset proportionally to the injected power thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.     

Reduced MHD equations with allowance for slow magnetosonic waves

The so-called reduced magnetohydrodynamics, which deals with the motion of incompressible fluids and is usually applied to describe plasma flows in a strong toroidal magnetic field, has a number of drawbacks and, in some cases, fails to produce correct results. The equations proposed here are simpler than the original MHD equations and are free of these drawbacks. These equations, like reduced MHD equations, make it possible to remove from consideration fast magnetosonic waves and to introduce the vector potential for the poloidal magnetic field. However, our equations differ from the reduced MHD equations in that they completely incorporate slow magnetosonic waves, the specific features of the toroidal geometry, and the effects of the toroidal velocity.     

Isodynamic axisymmetric equilibrium near the magnetic axis

Plasma equilibrium near the magnetic axis of an axisymmetric toroidal magnetic confinement system is described in orthogonal flux coordinates. For the case of a constant current density in the vicinity of the axis and magnetic surfaces with nearly circular cross sections, expressions for the poloidal and toroidal magnetic field components are obtained in these coordinates by using expansion in the reciprocal of the aspect ratio. These expressions allow one to easily derive relationships between quantities in an isodynamic equilibrium, in which the absolute value of the magnetic field is constant along the magnetic surface (Palumbo’s configuration).     

Influence of plasma pedestal profiles on access to ELM-free regimes in ITER

The influence of current density and pressure gradient profiles in the pedestal on the access to the regimes free from edge localized modes (ELMs) like quiescent H-mode in ITER is investigated. Using the simulator of MHD modes localized near plasma boundary based on the KINX code, calculations of the ELM stability were performed for the ITER plasma in scenarios 2 and 4 under variations of density and temperature profiles with the self-consistent bootstrap current in the pedestal. Low pressure gradient values at the separatrix, the same position of the density and temperature pedestals and high poloidal beta values facilitate reaching high current density in the pedestal and a potential transition into the regime with saturated large scale kink modes. New version of the localized MHD mode simulator allows one to compute the growth rates of ideal peeling-ballooning modes with different toroidal mode numbers and to determine the stability region taking into account diamagnetic stabilization. The edge stability diagrams computations and sensitivity studies of the stability limits to the value of diamagnetic frequency show that diamagnetic stabilization of the modes with high toroidal mode numbers can help to access the quiescent H-mode even with high plasma density but only with low pressure gradient values at the separatrix. The limiting pressure at the top of the pedestal increases for higher plasma density. With flat density profile the access to the quiescent H-mode is closed even with diamagnetic stabilization taken into account, while toroidal mode numbers of the most unstable peeling-ballooning mode decrease from n = 10?40 to n = 3?20.     

Experimental study and numerical simulation of ion cyclotron heating of a hydrogen plasma in the T-11M tokamak

Results are presented from investigations of the possibility of heating a hydrogen plasma at the fundamental harmonic of the ion cyclotron frequency in the T-11M tokamak. The fluxes of charge-exchange atoms that escape from the plasma in the radial direction and across the toroidal magnetic field (transverse neutrals) were recorded by a Lakmus neutral particle analyzer. Measurements by the analyzer show that, during an RF pulse, the ion temperature increases by approximately 50–100 eV. Such plasma parameters as the ion temperature, rotation velocity, and isotopic composition were measured by a high-resolution spectrometer. According to the data from high-resolution spectroscopy, the ion temperature increases by approximately 150 eV. Results from numerical simulations of the ion cyclotron resonance heating of a hydrogen plasma in the T-11M tokamak are also given.     

Interplay between intrinsic plasma rotation and magnetic island evolution in disruptive discharges

The behavior of the intrinsic toroidal rotation of the plasma column during the growth and eventual saturation of m/n = 2/1 magnetic islands, triggered by programmed density rise, has been carefully investigated in disruptive discharges in TCABR. The results show that, as the island starts to grow and rotate at a speed larger than that of the plasma column, the angular frequency of the intrinsic toroidal rotation increases and that of the island decreases, following the expectation of synchronization. As the island saturates at a large size, just before a major disruption, the angular speed of the intrinsic rotation decreases quite rapidly, even though the island keeps still rotating at a reduced speed. This decrease of the toroidal rotation is quite reproducible and can be considered as an indicative of disruption.